An efficient methodology for robustness evaluation by advanced interval analysis using updated second-order Taylor series expansion

An enhanced and efficient methodology for interval analysis is proposed to evaluate the robustness of an uncertain structure. While a basic assumption of “inclusion monotonic” is introduced in some of the interval analyses, the possibility is taken into account of occurrence of the extreme value of the objective function in an inner domain of interval parameters. It is shown that the critical combination of interval parameters can be derived explicitly so as to maximize the objective function by second-order Taylor series expansion. Two different approaches, called the FRP (Fixed Reference-Point) method and the URP (Updated Reference-Point) method, are proposed to obtain such a critical combination of interval parameters. The method is applied to building structures with passive dampers sustained by flexible supports. The objective function is given by the sum of the mean squares of interstorey drifts under random input. The damper capacity, its supporting member stiffness and building storey stiffness are taken as interval parameters. In order to investigate the validity of the proposed methods, numerical analyses are conducted for 2- and 20-storey building models including passive dampers. By comparing the results with the reference solution and those by other conventional methods, it is demonstrated that the URP method can provide the most accurate response bounds without hard computational effort.